About: Small perturbations of initial conditions of solutions of the Navier-Stokes equations in the L 3 -norm and applications

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About: Small perturbations of initial conditions of solutions of the Navier-Stokes equations in the L 3 -norm and applications Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper, we solve two problems. We prove a theorem on the stability of a strong solution with respect to the norm $\|cdot\|_{L^2}+\|cdot\|_{L^3}$\|\|.\|\|L2+\|\|.\|\|L3 in Section 2. Then, in Section 3, we show that there exist strong solutions of the Navier-Stokes initial-boundary value problem such that their initial values are arbitrarily large (in the norm of $scr D(A^{1/4})$D(A1/4)) and they belong to an arbitrarily chosen open set $Usubsetscr D(A^{1/2})$UcD(A1/2) at a time instant $xi>0$ξ>0 that can be as small as we wish (we denote by $A$A the Stokes operator). In this paper, we solve two problems. We prove a theorem on the stability of a strong solution with respect to the norm $\|cdot\|_{L^2}+\|cdot\|_{L^3}$\|\|.\|\|L2+\|\|.\|\|L3 in Section 2. Then, in Section 3, we show that there exist strong solutions of the Navier-Stokes initial-boundary value problem such that their initial values are arbitrarily large (in the norm of $scr D(A^{1/4})$D(A1/4)) and they belong to an arbitrarily chosen open set $Usubsetscr D(A^{1/2})$UcD(A1/2) at a time instant $xi>0$ξ>0 that can be as small as we wish (we denote by $A$A the Stokes operator). (en)
Title	Small perturbations of initial conditions of solutions of the Navier-Stokes equations in the L 3 -norm and applications Small perturbations of initial conditions of solutions of the Navier-Stokes equations in the L 3 -norm and applications (en)
skos:prefLabel	Small perturbations of initial conditions of solutions of the Navier-Stokes equations in the L 3 -norm and applications Small perturbations of initial conditions of solutions of the Navier-Stokes equations in the L 3 -norm and applications (en)
skos:notation	RIV/68407700:21110/10:00178201!RIV13-MSM-21110___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190612), Z(MSM6840770010)
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Kučera, Petr
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta stavební
http://linked.open...dnocenehoVysledku	287961
http://linked.open...ai/riv/idVysledku	RIV/68407700:21110/10:00178201
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Navier-Stokes equations; Stokes operator (en)
http://linked.open.../riv/klicoveSlovo	Stokes operator Navier-Stokes equations
http://linked.open...ontrolniKodProRIV	[C47925AEBFA0]
http://linked.open...v/mistoKonaniAkce	Estoril
http://linked.open...i/riv/mistoVydani	Berlin
http://linked.open...i/riv/nazevZdroje	Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Regularity and other qualitative properties of solutions to the Navier-Stokes and related equations, transition to turbulence.
http://linked.open...UplatneniVysledku	2010
http://linked.open...iv/tvurceVysledku	Kučera, Petr
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open...ain/vavai/riv/wos	000289445900020
http://linked.open.../riv/zahajeniAkce	2007-05-21 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Aplikovaná matematika v technických a fyzikálních vědách
number of pages	10 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-3-642-04068-9_20
http://purl.org/ne...btex#hasPublisher	Springer-Verlag
https://schema.org/isbn	978-3-642-04067-2
http://localhost/t...ganizacniJednotka	21110
is http://linked.open...avai/riv/vysledek of	Small perturbations of initial conditions of solutions of the Navier-Stokes equations in the L 3 -norm and applications

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